In the original Western set-covering model in Figure 6.22, we assumed that each city must be covered by at least one hub. Suppose that for added flexibility in flight routing, Western requires that each city must be covered by at least two hubs. How do the model and optimal solution change?

Figure 6.22

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A B D E F H K N P 1 Western Airlines hub location model 2 3 Input data: which cities are covered by which potential hubs Potential hub Range names used: Hubs_covered_by Total hubs Used_as_hub =Model$B$25:$B$ 36 =Model!$B$39 =Model!$B$21:$M$21 4 5 |City 6 JAT 7 IBO AT BO CH DE но LA NO NY PI SL SF SE 6 1 1 1 1 0. 1. 8 CH 0. 1. 1. 9 DE 1 1 0. 10 HO 0. 0. 1. 0. 0. 11 |LA 1. 12 INO 1. 1. 0. 13 NY 1. 14 PI 1 1. 0. 15 SL 1. 16 SF 17 SE 1 1. 1 18 19 Decisions: which cities to use as hubs 20 AT BO CH DE но LA NO NY PI SL SF SE 21 JUsed as hub 1. 1 1 22 23 Constraints that each city must be covered by at least one hub 24 City Hubs covered by Required 25 AT 2 1 >= 26 BO 1 27 CH 28 DE 1 >= 1 1 1 29 IHO 1 30 LA 31 INO 1 1 1 32 NY 1 33 PI 34 ISL >= 1 1. 1 35 ISE 1. 1. . 36 ISE 1 >= 1 37 38 Objective to minimize 39 Total hubs 3.